rm(list = ls())
library(Lahman)
package 㤼㸱Lahman㤼㸲 was built under R version 4.0.5
library(mosaic)
Registered S3 method overwritten by 'htmlwidgets':
method from
print.htmlwidget tools:rstudio
Registered S3 method overwritten by 'mosaic':
method from
fortify.SpatialPolygonsDataFrame ggplot2
The 'mosaic' package masks several functions from core packages in order to add
additional features. The original behavior of these functions should not be affected by this.
Attaching package: 㤼㸱mosaic㤼㸲
The following objects are masked from 㤼㸱package:dplyr㤼㸲:
count, do, tally
The following object is masked from 㤼㸱package:Matrix㤼㸲:
mean
The following object is masked from 㤼㸱package:ggplot2㤼㸲:
stat
The following objects are masked from 㤼㸱package:stats㤼㸲:
binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test, quantile, sd, t.test, var
The following objects are masked from 㤼㸱package:base㤼㸲:
max, mean, min, prod, range, sample, sum
library(tidyr)
package 㤼㸱tidyr㤼㸲 was built under R version 4.0.5
Attaching package: 㤼㸱tidyr㤼㸲
The following objects are masked from 㤼㸱package:Matrix㤼㸲:
expand, pack, unpack
library(tidyverse)
Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
-- Attaching packages ------------------------------------------------------------------------- tidyverse 1.3.0 --
v tibble 3.1.0 v stringr 1.4.0
v readr 1.4.0 v forcats 0.5.0
v purrr 0.3.4
package 㤼㸱tibble㤼㸲 was built under R version 4.0.5-- Conflicts ---------------------------------------------------------------------------- tidyverse_conflicts() --
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library(dplyr)
library(mplot)
package 㤼㸱mplot㤼㸲 was built under R version 4.0.5
Attaching package: 㤼㸱mplot㤼㸲
The following object is masked from 㤼㸱package:mosaic㤼㸲:
mplot
library(ggplot2)
library(factoextra)
package 㤼㸱factoextra㤼㸲 was built under R version 4.0.5Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
=======
<<<<<<< HEAD
=======
>>>>>>> b04cb5b5957a3ed2fb8943798fee8dafe331c80c
rm(list = ls())
library(Lahman)
library(mosaic)
library(tidyr)
library(tidyverse)
library(dplyr)
library(mplot)
library(ggplot2)
<<<<<<< HEAD
library(cluster)
library(factoextra)
package 㤼㸱factoextra㤼㸲 was built under R version 4.0.5Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
=======
library(factoextra)
>>>>>>> b04cb5b5957a3ed2fb8943798fee8dafe331c80c
>>>>>>> 8030880174c02db7595f2301b21b1b667ae0c4d4
#Load in People, Batting, and Pitching Dataframes
data("People")
data("Batting")
data("Pitching")
#Merges player name to Batting data.
bstats <- battingStats()
str(bstats)
'data.frame': 108789 obs. of 29 variables:
$ playerID: chr "abercda01" "addybo01" "allisar01" "allisdo01" ...
$ yearID : int 1871 1871 1871 1871 1871 1871 1871 1871 1871 1871 ...
$ stint : int 1 1 1 1 1 1 1 1 1 1 ...
$ teamID : Factor w/ 149 levels "ALT","ANA","ARI",..: 136 111 39 142 111 56 111 24 56 24 ...
$ lgID : Factor w/ 7 levels "AA","AL","FL",..: 4 4 4 4 4 4 4 4 4 4 ...
$ G : int 1 25 29 27 25 12 1 31 1 18 ...
$ AB : int 4 118 137 133 120 49 4 157 5 86 ...
$ R : int 0 30 28 28 29 9 0 66 1 13 ...
$ H : int 0 32 40 44 39 11 1 63 1 13 ...
$ X2B : int 0 6 4 10 11 2 0 10 1 2 ...
$ X3B : int 0 0 5 2 3 1 0 9 0 1 ...
$ HR : int 0 0 0 2 0 0 0 0 0 0 ...
$ RBI : int 0 13 19 27 16 5 2 34 1 11 ...
$ SB : int 0 8 3 1 6 0 0 11 0 1 ...
$ CS : int 0 1 1 1 2 1 0 6 0 0 ...
$ BB : int 0 4 2 0 2 0 1 13 0 0 ...
$ SO : int 0 0 5 2 1 1 0 1 0 0 ...
$ IBB : int NA NA NA NA NA NA NA NA NA NA ...
$ HBP : int NA NA NA NA NA NA NA NA NA NA ...
$ SH : int NA NA NA NA NA NA NA NA NA NA ...
$ SF : int NA NA NA NA NA NA NA NA NA NA ...
$ GIDP : int 0 0 1 0 0 0 0 1 0 0 ...
$ BA : num 0 0.271 0.292 0.331 0.325 0.224 0.25 0.401 0.2 0.151 ...
$ PA : num 4 122 139 133 122 49 5 170 5 86 ...
$ TB : num 0 38 54 64 56 15 1 91 2 17 ...
$ SlugPct : num 0 0.322 0.394 0.481 0.467 0.306 0.25 0.58 0.4 0.198 ...
$ OBP : num 0 0.295 0.302 0.331 0.336 0.224 0.4 0.447 0.2 0.151 ...
$ OPS : num 0 0.617 0.696 0.812 0.803 ...
$ BABIP : num 0 0.271 0.303 0.326 0.328 0.229 0.25 0.404 0.2 0.151 ...
People$name <- paste(People$nameFirst, People$nameLast, sep = " ")
batting_name <- merge(Batting,
People[,c("playerID", "name")],
by = "playerID", all.x = TRUE)
#Merges player name to Pitching data.
People$name <- paste(People$nameFirst, People$nameLast, sep = " ")
pitching_name <- merge(Pitching,
People[,c("playerID", "name")],
by = "playerID", all.x = TRUE)
#Creating additional stats for bstats
bstats[is.na(bstats)] = 0
bstats <- bstats %>%
mutate(K_Percent = SO / PA) %>%
mutate(BB_Percent = (BB + IBB) / PA)
#Keep players with over 150 at bats. (We can change this value if necessary).
#Creating batting average variable.
batting <- bstats %>%
filter(AB >= 150)
Lessons 1 and 2 will just be parts of the overall project. Simple things like data manipulation, apply functions, boxplots, etc. This will be data preparation items and exploratory analysis.
b <- ggplot(batting, aes(x = teamID, y = HR)) +
geom_boxplot(col = "black", aes(fill = teamID))
b
<<<<<<< HEAD
hitters1 <- batting %>%
filter(yearID < 1895) %>%
select(SlugPct)
hitters2 <- batting %>%
filter(yearID > 1894, yearID < 1921) %>%
select(SlugPct)
hitters3 <- batting %>%
filter(yearID > 1920, yearID < 1969) %>%
select(SlugPct)
hitters4 <- batting %>%
filter(yearID > 1969) %>%
select(SlugPct)
#Organizing 4 different datasets looking at slugging percentage for the following boxplots. All of these are somewhat different eras, with the most dramatic split being from before 1920 (pre-Babe Ruth) and after 1920 (during and post-Babe Ruth)
boxplot(hitters1,
main = "Slugging percentage from late 1871 - 1894",
ylab = "Slugging percentage",
col = "blue",
horizontal = TRUE)
<<<<<<< HEAD
boxplot(hitters2,
main = "Slugging percentage from 1895-1920",
ylab = "Slugging percentage",
col = "yellow",
horizontal = TRUE)
<<<<<<< HEAD
boxplot(hitters3,
main = "Slugging percentage from 1921-1968",
ylab = "Slugging percentage",
col = "red",
horizontal = TRUE)
<<<<<<< HEAD
boxplot(hitters4,
main = "Slugging percentage from 1969 - present",
ylab = "Slugging percentage",
col = "red",
horizontal = TRUE)
<<<<<<< HEAD
sapply(hitters1, mean, na.rm = T)
SlugPct
0.3456088
sapply(hitters2, mean, na.rm = T)
SlugPct
0.348923
sapply(hitters3, mean, na.rm = T)
SlugPct
0.3972127
sapply(hitters4, mean, na.rm = T)
SlugPct
0.4088045
#Notice that gigantic increase between hitters2 and hitters3
summary(hitters1)
SlugPct
Min. :0.1220
1st Qu.:0.2900
Median :0.3380
Mean :0.3456
3rd Qu.:0.3970
Max. :0.6960
summary(hitters2)
SlugPct
Min. :0.1480
1st Qu.:0.3003
Median :0.3430
Mean :0.3489
3rd Qu.:0.3910
Max. :0.8490
summary(hitters3)
SlugPct
Min. :0.1760
1st Qu.:0.3420
Median :0.3900
Mean :0.3972
3rd Qu.:0.4440
Max. :0.8460
<<<<<<< HEAD
=======
summary(hitters4)
SlugPct
Min. :0.1730
1st Qu.:0.3540
Median :0.4040
Mean :0.4088
3rd Qu.:0.4580
Max. :0.8630
>>>>>>> b04cb5b5957a3ed2fb8943798fee8dafe331c80c
<<<<<<< HEAD
summary(hitters4)
SlugPct
Min. :0.1730
1st Qu.:0.3540
Median :0.4040
Mean :0.4088
3rd Qu.:0.4580
Max. :0.8630
=======
>>>>>>> b04cb5b5957a3ed2fb8943798fee8dafe331c80c
#Keep batting stats that we want for pairs.
batting_num <- bstats %>%
select('BA', 'PA', 'SlugPct', "OBP", "SO", "HR")
pairs(batting_num)
<<<<<<< HEAD
careerBatting <- na.omit(bstats)
careerBatting <- careerBatting %>%
group_by(playerID) %>%
summarise(across(everything(), mean, na.rm = TRUE))
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is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: 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numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning NAargument is not numeric or logical: returning 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pairs()
res <- batting_num %>% prcomp(scale = TRUE)
res
loadings <- res$rotation
loadings
score_mat <- res$x
score_mat
get_eig(res)
get_eig(res) %>%
ggplot(aes(x = 1:6, y = cumulative.variance.percent)) +
geom_line() +
geom_point() +
geom_hline(yintercept = 80) +
xlab("Principal Component") +
ylab("Proportion of Variance Explained") +
ggtitle("Scree Plot of Principal Component for Batting Statistics")
2 Principal Components: PC1 and PC2
fviz_screeplot(res, main = "Scree Plot")
Can Identify an elbow in 3.
res %>%
fviz_pca_var(axes = c(1,2),
col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE
)
eu_dist <- get_dist(hitters4, method = 'euclidean')
hc_complete <- hclust(eu_dist, method='complete')
plot(hc_complete)